Introduction

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Welcome!

This website provides interactive results for the forecasting models explored in the paper Estimating Neighborhood Rents using Scraped Data.

The goal of this research is to a.) understand the temporal dynamics of rent estimates in Seattle and b.) forecast the current quarter’s rent levels based off of the prior periods. The focal series of models regress median one-bedroom rent asked values on different specifications of the panel’s correlation structure (i.e. temporal and spatial). All of the candidate models’ posterior distributions are estimated with integrated nested Laplace approximations (INLA) using the default, weakly-informative priors for all model hyperparameters. Throughout the following analyses, the training data are 2017 Q1 up to the prior quarter (i.e. 2018 Q1). The test period is a forecast for the current period and includes comparison to the appropriate median rent estimates for data observed so far in this period.

Most graphics include some level of interactivity, usually either hover-over tooltip information or a slider to control various views of the graphic. Clicking on cases will highlight data elements in most graphics, and double-clicking will reset the graphic.

This page was last updated: 2018-06-04




Table of Contents

Page Description
Distribution density graphic to investigate the distribution of rents among Seattle neighborhoods for each quarter
Panel Time-Series line graphic to show the observed or modeled temporal structure
Spatial Time-Series series of maps to show observed change across time
Model Fit tables of model root mean square error (RMSE), mean absolute error (MAE), and deviance information criterion (DIC) across training and test data

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Observed vs. Smoothed Rent Estimates

Distribution

Panel Time-Series

Spatial Time-Series

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Observed

Non-Spatial AR(1)

Spatial AR(1)

Spatiotemporal AR(1)

Model Fit

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Model Legend

Model abbr. Description
int Quarter fixed intercept
log(med1B) ~ 1 + Qtr
ns Non-spatial tract random effect for each tract, quarter fixed intercept
log(med1B) ~ 1 + Qtr + f(idtract, model = “iid”)
nsar1 Non-spatial tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter
log(med1B) ~ 1 + f(idtract, model = “iid”) + f(idqtr, model = “ar1”) + , f(idqtr1, model = “iid”)
bym Spatial intrinsic conditional autoregressive (ICAR) tract random-effect, non-spatial i.i.d tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter
log(med1B) ~ 1 + f(idtract, model = “bym”, scale.model = T, graph = “../output/seatract.graph”) + , f(idqtr, model = “ar1”) + f(idqtr1, model = “iid”)
spt Spatial intrinsic conditional autoregressive (ICAR) tract random-effect, non-spatial i.i.d tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter, i.i.d. random effect for tract-quarter (space-time interaction)
log(med1B) ~ 1 + f(idtract, model = “bym”, scale.model = T, graph = “../output/seatract.graph”) + , f(idqtr, model = “ar1”) + f(idqtr1, model = “iid”) + f(idtractqtr, , model = “iid”)

Accuracy and Information Criteria

train_test int_rmse ns_rmse nsar1_rmse bym_rmse spt_rmse
Test 306.1430 213.8335 206.3276 199.2226 199.3008
Training 324.2904 145.9141 145.9562 147.2808 146.1517



train_test int_mae ns_mae nsar1_mae bym_mae spt_mae
Test 250.5052 151.4203 148.5778 141.9294 141.8590
Training 261.4572 100.9766 100.6866 102.3140 101.5464



train_test int_DIC ns_DIC nsar1_DIC bym_DIC spt_DIC
Training -230.4437 -872.8757 -871.7695 -874.5002 -876.1002



train_test int_WAIC ns_WAIC nsar1_WAIC bym_WAIC spt_WAIC
Training -230.0655 -845.3891 -844.3364 -847.7388 -848.6378

Hyperparameters

Non-Spatial AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 94.4504 6.3451 82.3883 94.3203 107.3392 94.1694
Precision for idtract 30.7244 4.2509 23.1165 30.4724 39.8230 30.0119
Precision for idqtr 3704.6708 3774.0461 555.1018 2589.2781 13619.6753 1361.1160
Rho for idqtr 0.2605 0.3581 -0.4721 0.2856 0.8484 0.3946
Precision for idqtr1 14301.7423 17584.8007 273.1949 8209.2304 61744.3916 355.9311



Spatial AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 93.8396 6.3354 81.9253 93.6523 106.8628 93.3166
Precision for idtract (iid component) 89.5463 21.5290 54.3086 87.1808 138.5956 82.6906
Precision for idtract (spatial component) 91.2776 29.2072 47.3106 86.8532 160.7809 78.6878
Precision for idqtr 3524.4233 3566.1799 525.0535 2472.2245 12897.8680 1299.0853
Rho for idqtr 0.2678 0.3562 -0.4665 0.2951 0.8491 0.4120
Precision for idqtr1 14890.5041 18182.3908 309.0561 8654.5605 64109.6510 435.4857



Spatiotemporal AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 94.1979 6.4074 82.2339 93.9796 107.4283 93.5481
Precision for idtract (iid component) 90.4211 21.9208 54.2227 88.1708 139.8528 83.9196
Precision for idtract (spatial component) 90.8292 29.2135 47.4284 86.1470 160.9404 77.6065
Precision for idqtr 3934.7623 4056.5311 591.5222 2733.0549 14575.3765 1435.8137
Rho for idqtr 0.2644 0.3553 -0.4643 0.2899 0.8468 0.3988
Precision for idqtr1 13548.1889 16961.1277 227.0836 7589.8856 58837.4716 260.2503
Precision for idtractqtr 18663.7171 18340.9069 1384.8908 13300.3879 66908.9743 3855.6510

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Non-Spatial AR(1)

Spatial AR(1)

Spatiotemporal AR(1)